Question: Solve for $x$ : $8\sqrt{x} - 1 = 4\sqrt{x} + 10$
Solution: Subtract $4\sqrt{x}$ from both sides: $(8\sqrt{x} - 1) - 4\sqrt{x} = (4\sqrt{x} + 10) - 4\sqrt{x}$ $4\sqrt{x} - 1 = 10$ Add $1$ to both sides: $(4\sqrt{x} - 1) + 1 = 10 + 1$ $4\sqrt{x} = 11$ Divide both sides by $4$ $\frac{4\sqrt{x}}{4} = \frac{11}{4}$ Simplify. $\sqrt{x} = \dfrac{11}{4}$ Square both sides. $\sqrt{x} \cdot \sqrt{x} = \dfrac{11}{4} \cdot \dfrac{11}{4}$ $x = \dfrac{121}{16}$